Quantum mechanics of single molecules

Rok, strany: 1997, 159 - 178

In traditional quantum mechanics, a density operator (non-pure state) cannot uniquely be decomposed into pure states and different decompositions are considered as being equivalent. Here it is argued that different decompositions of a thermal non-pure state sometimes refer to entirely different physical situations, as, for example, to molecules with or without nuclear structure. Among all the infinitely many different decompositions of a thermal state the most stable one (under external stochastic perturbations) is chosen. It is argued that this stable decomposition is uniquely determined by a maximum entropy principle in the sense of Jaynes.

This individual approach to quantum mechanics is checked for the quantum-mechanical Curie-Weiss model of a magnent. The question there is how “fast'' the specific magnetization gets a classical observable and how ”fast“ the superpositions of states with opposite permanent magnetization “die out” with increasing number $N$ of spins. This increasingly classical behaviour is described here by a large-deviation entropy, compatible with the usual limit $N\to∞$ of algebraic quantum mechanics. For finite $N$, the superposition principle is still universally valid and nevertheless an approximate classical observable ”magnetization“ appears, becoming strictly classical in the limit $N=∞$. It is argued that usual statistical (algebraic) quantum mechanics imposes too excessive conditions on symmetry breaking and classical structures (arising only in the limit of infinitely many degrees of freedom).

ISO 690:

Amann, A. 1997. Quantum mechanics of single molecules. In Tatra Mountains Mathematical Publications, vol. 10, no.1, pp. 159-178. 1210-3195.

APA:

Amann, A. (1997). Quantum mechanics of single molecules. Tatra Mountains Mathematical Publications, 10(1), 159-178. 1210-3195.